Is it permissible to remove the manufacturer's name from high-quality cooling devices (air conditioners) and replace it with another name, or leave it without a name, with the aim of preventing commercial competition?

There appears to be no impediment to removing the manufacturer's name if this does not involve deception or fraud towards the manufacturer or the buyer. The manufacturer might be harmed if they rely on their name appearing for promotion, and the buyer might be deceived if the name is removed and the company's reputation is poor. If there is no deception of the buyer or an illusion that it was manufactured by a better company, then there is no harm in that. It is preferable to reach an agreement with the manufacturer.